Full waveform inversion with nonlocal similarity and model-derivative domain adaptive sparsity-promoting regularization

Abstract: Full waveform inversion (FWI) is a highly nonlinear and ill-posed problem. On one hand, it can be easily trapped in a local minimum. On the other hand, the inversion results may exhibit strong artifacts and reduced resolution because of inadequate constraint from data. Proper regularizations are necessary to reduce such artifacts and steer the inversion towards a good direction. In this study, we propose a novel adaptive sparsity-promoting regularization for FWI in the model-derivative domain which exploits nonlocal similarity in the model. This regularization can be viewed as a generalization of total variation (TV) with multi-class learning-based dictionaries. The dictionaries incorporate the prior information of nonlocal similarity into the inversion, exploiting the fact that geological patterns at different places are similar to some others up to affine transformations (translation, rotation and scaling). Such nonlocal similarity priors effectively reduce the degrees of freedom in model parameters, and may also mitigate the problem of local minima. The formulated optimization problem is solved by the Alternating Direction Method of Multipliers (ADMM). By interpreting the iterative scheme, we find our method closely connected with image processing techniques and convolutional neural networks (CNN). We test our proposed method on a modified BP 2004 velocity model and a smoothed Marmousi model. Compared with traditional FWI, our technique can better reconstruct sharp edges such as salt body boundaries, and is also able to effectively reduce artifacts. Compared with TV, our result is less blocky and more geologically realistic. Quantitatively, our result has the highest structural similarity index (SSIM) and also the lowest model mean square error.